Netz - The Shaping of Deduction.pdf - Theology, philosophy and the history of ideas - piotrzachu69

THE SHAPING OF

DEDUCTION IN GREEK

MATHEMATICS:

A Study in Cognitive History

Reviel Netz

Cambridge University Press

The aim of this book is to explain the shape of Greek mathemati-

cal thinking. It can be read on three levels: ﬁrst as a description of

the practices of Greek mathematics; second as a theory of the

emergence of the deductive method; and third as a case-study for

a general view on the history of science. The starting point for

the enquiry is geometry and the lettered diagram. Reviel Netz

exploits the mathematicians’ practices in the construction and let-

tering of their diagrams, and the continuing interaction between

text and diagram in their proofs, to illuminate the underlying

cognitive processes. A close examination of the mathematical use

of language follows, especially mathematicans’ use of repeated

formulae. Two crucial chapters set out to show how mathemati-

cal proofs are structured and explain why Greek mathematical

practice manages to be so satisfactory. A ﬁnal chapter looks into

the broader historical setting of Greek mathematical practice.

is a Research Fellow at Gonville and Caius

College, Cambridge, and an Afﬁliated Lecturer in the Faculty

of Classics.

Abbreviations

This Page Intentionally Left Blank

THE SHAPING OF DEDUCTION

IN GREEK MATHEMATICS

Edited by Q

( General Editor )

, W

, J. B. S

and J

The books in this series will discuss the emergence of intellectual traditions

and of related new disciplines. The procedures, aims and vocabularies that

were generated will be set in the context of the alternatives available within

the contemporary frameworks of ideas and institutions. Through detailed

studies of the evolution of such traditions, and their modiﬁcation by different

audiences, it is hoped that a new picture will form of the development of ideas

in their concrete contexts. By this means, artiﬁcial distinctions between the

history of philosophy, of the various sciences, of society and politics, and of

literature may be seen to dissolve.

The series is published with the support of the Exxon Foundation.

A list of books in the series will be found at the end of the volume .

Netz - The Shaping of Deduction.pdf